Question: Solve for $x$ and $y$ using elimination. ${-3x+y = -23}$ ${4x-y = 32}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-3x+y = -23}\thinspace$ to find $y$ ${-3}{(9)}{ + y = -23}$ $-27+y = -23$ $-27{+27} + y = -23{+27}$ ${y = 4}$ You can also plug ${x = 9}$ into $\thinspace {4x-y = 32}\thinspace$ and get the same answer for $y$ : ${4}{(9)}{ - y = 32}$ ${y = 4}$